A tug on the handle of a vending machine in Florida will yield any variety of snacks from sandwiches to coffee but all with a common distribution point -- Orlando.

Flowers Distributors of Florida Inc., a distributor of vending-machine products, has leased 20,000 square feet of warehouse and distribution space in the 33rd Street Industrial Park. Flowers Distributors of Florida is a subsidiary of Flowers Industries Inc., a Thomasville, Ga.-based bakery with sales of $700 million a year.

Flowers is a distributor of most vending-machine products, including soft drinks, sandwiches, gum and coffee, which will be distributed to 170 vending- machine operators in Florida, south Georgia and south Alabama, said Ken Shea, president of Flowers Distributors of Florida. Shea said those 170 operators represent several thousand vending machines.

The Orlando vending-machine food distribution center, which employs 16, is one of five east of the Mississippi for Flowers. Others are in Milwaukee, Wis., Columbus, Ohio, Petersburg, Va., and Memphis, Tenn.

Shea said Orlando was chosen because ''it is both accessible to the Miami market and the south Georgia-south Alabama markets.'' He said Central Florida is a growing market for vending-machine coffee and coffee supplies because of the increased business activity and office-space construction.

Walter Reed, spokesman for the Chicago-based National Automatic Merchandising Association, called Flowers a major player in the vending machine supply industry. ''Anyone that has 170 vending operators, is covering the market very well,'' said Reed, whose trade group has 2,200 members.

He said regional companies, such as Flowers, are ''dominating the supply end of the business. They don't mind shipping small orders on short notice. The larger, national companies won't do that.''

Four months ago, Flowers bought A-1 Kingsize Sandwich of Orlando. Shea said not only will A-1 provide Flowers with a supply of vending-machine sandwiches, it will also help break into the convenience-store market, which Shea refers to poetically as the ''mass-feeding'' business.